Simplify; express your answer in exponential form. Assume $z\neq 0, y\neq 0$. $\dfrac{{z^{2}y^{-1}}}{{(zy^{3})^{2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${z^{2}y^{-1} = z^{2}y^{-1}}$ On the left, we have ${z^{2}}$ to the exponent ${1}$ . Now ${2 \times 1 = 2}$ , so ${z^{2} = z^{2}}$ Apply the ideas above to simplify the equation. $\dfrac{{z^{2}y^{-1}}}{{(zy^{3})^{2}}} = \dfrac{{z^{2}y^{-1}}}{{z^{2}y^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{2}y^{-1}}}{{z^{2}y^{6}}} = \dfrac{{z^{2}}}{{z^{2}}} \cdot \dfrac{{y^{-1}}}{{y^{6}}} = z^{{2} - {2}} \cdot y^{{-1} - {6}} = y^{-7}$